Hypervolume-Guided Decomposition for Parallel Expensive Multiobjective Optimization

The hypervolume metric is widely used to guide the search in multiobjective optimization. However, in parallel expensive multiobjective optimization, the hypervolume-based multipoint expected improvement (EI) suffers from high computational overhead and scales poorly with the batch size. To address...

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Bibliographic Details
Published in:IEEE transactions on evolutionary computation 2024-04, Vol.28 (2), p.432-444
Main Authors: Zhao, Liang, Zhang, Qingfu
Format: Article
Language:English
Subjects:
Algorithms
Computational modeling
Decomposition
Design optimization
efficient global optimization (EGO)
expected improvement (EI)
expensive multiobjective optimization
hypervolume
Linear programming
Measurement
Multiple objective analysis
Optimization
Pareto optimization
Predictive models
Urban areas
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Summary:The hypervolume metric is widely used to guide the search in multiobjective optimization. However, in parallel expensive multiobjective optimization, the hypervolume-based multipoint expected improvement (EI) suffers from high computational overhead and scales poorly with the batch size. To address this issue, we integrate hypervolume-based EI with the MOEA/D framework and propose a novel EI, named the expected direction-based hypervolume improvement (DirHV-EI). The DirHV-EI only measures the hypervolume improvement within each axis-parallel box induced by the modified Tchebycheff scalarization. Thus, it has a simple analytical expression that can be easily computed. Theoretical analysis indicates that the maximization of our proposed improvement function can help to maximize both the weighted hypervolume and the Tchebycheff improvement metrics. Using DirHV-EI, we design a decomposition-based Bayesian optimization algorithm for solving expensive multiobjective optimization problems. At each iteration, the MOEA/D is used to maximize the DirHV-EI values with respect to a number of direction vectors in a collaborative manner, and a number of candidate solutions can be obtained. Then, a submodularity-based greedy selection strategy is used to select multiple query points from the candidates. Experimental results on both benchmark instances and real-world problems show that our proposed algorithm is an efficient and effective method for parallel expensive multiobjective optimization.
ISSN:1089-778X
1941-0026
DOI:10.1109/TEVC.2023.3265347